Statistical Analysis: Aluminum Manufacturing Industry Report Sample
based on a draft by
Statistical analysis was done on the aluminum manufacturing data. Using appropriate tests, some relationships were established. First, sheet metal grade aluminum has the highest production output at sections 1 and 2. However, the standard deviation values are also highest at these two sections. Second, there is evidence that the produced amount of electrical grade aluminum is significantly different (probably higher) than the sheet metal grade aluminum made. Third, there is evidence that the bauxite consumption the bauxite consumption is significantly different (probably higher) than the purchasing policy of 4.2 tons per pot. Lastly, power consumption increases as metal loss increases. The data can be modeled by the regression line y= 4.1139x + 11.5, where y is in 1000 kWhr and x is in % metal lost. The linear model captures 84.91% of the variability in data. Further analysis says that the model indicates a strong relationship since the slope is not equal to 0. Thus power consumption can be predicted using % metal loss per production run. Appropriate recommendations were then cite for each section.
Executive Summary 2
Aluminum is a metallic element with many essential applications to modern society. Its production involves the Hall-Heroult process. In this process, there is an electrochemical reduction of alumina (aluminum ore) in electrolyte bath. High temperature is needed at approximately 900 degree Celsius which makes aluminum production an energy extensive process. In this paper, a data analysis using Microsoft Excel is used in the aluminum production business perspective. The interplay of different process variables results in the economic feasibility of the production plant. Thus, they have to be considered and studied.
Data from an aluminum production facility is available for statistical analysis. It consists of random samples of pots from four sections of the production plant from the previous year. Data values include the inputs, outputs and other operation parameters. Raw materials such as: (1) carbon, (2) alumina, (3) cryolite, (4) bauxite, and (5) aluminum fluoride are the inputs to the process. Their consumption per batch is recorded thoroughly in the Excel spreadsheet provided. The product, which is the output of the process, can be classified into three types: (a) electrical grade, (b) chemical and plumbing grade, and (c) sheet metal grade. Furthermore, data is also available for the total production output and the percentage of metal lost inherent in the processing. Aside from the input and output, process variables such as power consumption, pot temperature, and current efficiency are also available.
2. Sheet Metal Grade
Based on the given data, the average aluminum production is highest for section number 1 at 0.415 tons and is lowest for section number 4 at 0.326 tons. The standard deviation was also highest for section numbers 1 and 2 at 0.048 tons and is lowest for section number 3 at 0.036 tons. This implies that the variability or the dispersion of data in sections 1 and 2 is highest while data for section 3 has the lowest variability among the four sections. The summary of the analysis is shown in Table 1. The table summarizes the average production per section and their corresponding standard deviation.
3. Electrical Grade versus Sheet Metal Grade Aluminum
Electrical grade aluminum and the sheet metal grade aluminum are produced by the same process. However, it is believed that the amount of electrical grade aluminum produced at the plant is different to the amount of sheet metal aluminum produced. To gain statistical evidence to support this claim, a paired z-test is made. Since the sample size n= 80 which is greater than 30, a z-test is more appropriate than a t-test. Furthermore, the population variance is also known. The data are paired such that the difference between the amount of electrical grade (x1) and sheet metal grade aluminum (x2) is tested for the corresponding hypotheses. The difference d = x1 - x2. The mean of the values of this difference is treated for z-test.
The details of the statistical test done are summarized in Table 2. The null hypothesis is Ho: µd = 0. This corresponds to the case where there is no significant difference between the two data sets (electrical grade and sheet metal). The alternative hypothesis is the case Ha: µd ≠ 0. This corresponds to the case where there is a significant difference between the two data sets. The next step in the analysis is the computation for the standard normal random variable Z, where z = (d – 0)/ (σ/n). From the given data, d = 0.091 tons, σ = 0.056, and n = 80. The calculated z-value is 14.53. Next, the rejection region is determined. A level of significance (α) of 0.05 is used assuming a confidence level of 95%. From the z-distribution table, z (α/2 = 0.025) = 1.96. The rejection region is therefore | z | > 1.96.
The calculated z-value is 14.53 > 1.96. The decision made is to reject the null hypothesis and accept the alternative hypothesis. There is evidence that the difference between the amounts of electrical grade and sheet metal aluminum is not equal to 0. This means that there is significant difference between values of production of these two products per pot.
4. Bauxite Consumption Purchasing Policy
The plant manager is required to determine the amount of bauxite to purchase. Current purchasing decisions are based upon an average bauxite consumption of 4.2 tons per pot. Using a level of significance (α) at 0.05, this policy value is tested if it is still appropriate. Too high bauxite inventory means additional inventory cost while too low inventory levels could also lead to shortage of raw materials during the production run. A z-test is made to test the hypothesis that average bauxite consumption is still 4.2 tons/ pot since the variance is known and the sample size is greater than 30.
The results of this analysis are summarized in Table 3. The first step is the setting up of the null and alternative hypotheses. The mean (µ) used in this section is the average bauxite consumption per pot from the 80 random samples. The null hypothesis is Ho: µ = 4.2. The alternative hypothesis is Ha: µ ≠ 4.2. From the given data, x = 4.505 tons, σ = 0.055, and n = 80. Then, the standard normal random variable Z is computed. Z = (x – 4.2)/ (σ/n) = (4.505 – 4.2)/ (0.055/80 ) = 49.60. The rejection region is based on a two-tailed test at α=0.05. z (α/2 = 0.025) = 1.96. Thus, the rejection region is | z | > 1.96. Since the computed z = 49.60 > 1.96, the null hypothesis is rejected. There is evidence that the true bauxite consumption per pot is different from the purchasing policy of 4.2 tons/ pot. Data suggests that the true bauxite consumption per batch is even higher than 4.2 tons.
There are two possible reasons for this scenario which justifies two possible courses of actions. One reason is that there are significant wastages of bauxite in the production process. A solution for this could be the creation of a problem-solving team to study current line practices. However, this has to be verified. Another reason would be that the standard raw material requirement (RMR) in the policy needs updating against current batching methods. There is a need to change the standard RMR for bauxite in order to avoid depletion of inventory during future production runs.
5. Metal Losses and Power Consumption
The aluminum production company believes that high metal losses are associated with more energy consumed. Data in terms of power consumption (in x1000 kWh) and metal loss (%) are provided. Since power consumption mainly determines the economic feasibility of the overall process, it is the dependent variable (y) in the analysis. Thus, the percentage metal loss is the independent variable (x). Using the given data, a scatter plot is made with metal loss in the horizontal axis and power consumption on the vertical axis.
Using the Trendline option in Microsoft Excel, a least squares line is plotted in the same scatter plot (See Figure 1). The resulting linear function is y = 4.1139x + 11.5. The coefficient 4.1339 is the slope of the line. It has a positive value which means that as metal loss increases, power consumption also increase. With every 1% metal loss increase, power consumption increases by 4,113.9 kWhr. The y-intercept of the line is 11.5. This means that at 0% metal loss, the power consumption is at lowest 11,500 kWhr. However, as can be seen in Figure 1, the lowest metal loss achieved based on past data is approximately 16%. This will be a challenge to the production team and even to the technology involved to further lessen this % metal loss.
Figure 1: Plot of Power Consumption versus Metal Loss
Although some of the data points in the plot are somewhere at the top or bottom of the regression line, there is an adequate fit to the data based on the graphical perspective. The R2 or the correlation coefficient is 0.8491. This means that 84.91% of the data is modeled by the least squares line.
Using the regression equation, the predicted power consumption y = 4.1139x + 11.5. For pot 215, the metal loss is 19.76%. Thus, the predicted y = 12,313 kWhr. At metal loss = 25%, predicted y = 12,528 kWhr. Also at metal loss = 33%, predicted y = 12,858 kWhr. Generally, as metal loss increases, power consumption increases. It is best to decrease metal loss at lesser than 19.76% to have less power consumption. This results in more efficient process with regards to less resources needed to run the production process.
8. Conclusion and recommendations
Based on the statistical analyses made on the data, these are the general results:
There is evidence that the difference between the amounts of electrical grade and sheet metal aluminum is not equal to 0. Data suggest that the produced amount of electrical grade aluminum is significantly different (probably higher) than the sheet metal grade aluminum made.
There is evidence that the bauxite consumption is significantly different from the purchasing policy of 4.2 tons. Based on the statistical analysis made, the bauxite consumption is significantly different (probably higher) than the purchasing policy of 4.2 tons per pot.
Based on the plot of power consumption versus metal loss, power consumption increases as metal loss increases. The data can be modeled by the regression line y= 4.1139x + 11.5, where y is in 1000 kWhr and x is in % metal lost. The linear model captures 84.91% of the variability in data. Further analysis says that the model indicates a strong relationship since B is not equal to 0. Thus power consumption can be predicted using % metal loss per production run.